generalized extreme value (GEV) distribution for single variable
alex lin
November 08, 2024
GEV for single variable
FortNelson
maxEHF
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.46 0.12 0.12 0.04 0.34
## ab 0.46 1.00 0.04 0.28 0.33 0.69
## fn 0.12 0.04 1.00 0.13 0.09 0.08
## ke 0.12 0.28 0.13 1.00 0.39 0.34
## pg 0.04 0.33 0.09 0.39 1.00 0.49
## yv 0.34 0.69 0.08 0.34 0.49 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 829.6514
##
## Estimates
## loc scale shape
## 25.0600 22.8921 0.3011
##
## Standard Errors
## loc scale shape
## 2.9647 2.5235 0.1194
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 27
## Gradient Evaluations: 15
##
##
## Tail behavior based on shape parameter (0.301): Heavy-tailed
avgexc
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.18 0.19 0.34 0.02 0.16
## ab 0.18 1.00 -0.04 0.20 0.43 0.59
## fn 0.19 -0.04 1.00 0.07 0.16 0.07
## ke 0.34 0.20 0.07 1.00 0.24 0.26
## pg 0.02 0.43 0.16 0.24 1.00 0.33
## yv 0.16 0.59 0.07 0.26 0.33 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 378.6132
##
## Estimates
## loc scale shape
## 4.5968 2.1678 -0.2201
##
## Standard Errors
## loc scale shape
## 0.25992 0.18320 0.06957
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 35
## Gradient Evaluations: 13
##
##
## Tail behavior based on shape parameter (-0.22): Short-tailed
total precipitation
##
## Spearman correlation matrix
## year fn ab ke pg yv
## year 1.00 0.15 -0.05 0.04 -0.10 0.02
## fn 0.15 1.00 0.11 0.07 0.16 0.13
## ab -0.05 0.11 1.00 0.55 0.25 0.87
## ke 0.04 0.07 0.55 1.00 0.29 0.53
## pg -0.10 0.16 0.25 0.29 1.00 0.35
## yv 0.02 0.13 0.87 0.53 0.35 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 575.3943
##
## Estimates
## loc scale shape
## 20.5750 12.4311 0.0241
##
## Standard Errors
## loc scale shape
## 1.67036 1.22451 0.08565
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 15
## Gradient Evaluations: 6
##
##
## Tail behavior based on shape parameter (0.024): Heavy-tailed
YVR
Assess trend for EHF
maxEHF
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.46 0.12 0.12 0.04 0.34
## ab 0.46 1.00 0.04 0.28 0.33 0.69
## fn 0.12 0.04 1.00 0.13 0.09 0.08
## ke 0.12 0.28 0.13 1.00 0.39 0.34
## pg 0.04 0.33 0.09 0.39 1.00 0.49
## yv 0.34 0.69 0.08 0.34 0.49 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 576.283
##
## Estimates
## loc scale shape
## 6.9468 5.5791 0.1645
##
## Standard Errors
## loc scale shape
## 0.67927 0.52708 0.08107
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 33
## Gradient Evaluations: 11
##
##
## Tail behavior based on shape parameter (0.164): Heavy-tailed
total precipitation
##
## Spearman correlation matrix
## year fn ab ke pg yv
## year 1.00 0.15 -0.05 0.04 -0.10 0.02
## fn 0.15 1.00 0.11 0.07 0.16 0.13
## ab -0.05 0.11 1.00 0.55 0.25 0.87
## ke 0.04 0.07 0.55 1.00 0.29 0.53
## pg -0.10 0.16 0.25 0.29 1.00 0.35
## yv 0.02 0.13 0.87 0.53 0.35 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 761.5605
##
## Estimates
## loc scale shape
## 94.85863 49.52703 -0.07152
##
## Standard Errors
## loc scale shape
## 6.62907 4.70419 0.08397
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 35
## Gradient Evaluations: 22
##
##
## Tail behavior based on shape parameter (-0.072): Short-tailed
avgexc
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.18 0.19 0.34 0.02 0.16
## ab 0.18 1.00 -0.04 0.20 0.43 0.59
## fn 0.19 -0.04 1.00 0.07 0.16 0.07
## ke 0.34 0.20 0.07 1.00 0.24 0.26
## pg 0.02 0.43 0.16 0.24 1.00 0.33
## yv 0.16 0.59 0.07 0.26 0.33 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 286.0057
##
## Estimates
## loc scale shape
## 2.138 1.286 -0.215
##
## Standard Errors
## loc scale shape
## 0.15040 0.09905 0.04432
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 50
## Gradient Evaluations: 12
##
##
## Tail behavior based on shape parameter (-0.215): Short-tailed
Kelowna
maxEHF
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.46 0.12 0.12 0.04 0.34
## ab 0.46 1.00 0.04 0.28 0.33 0.69
## fn 0.12 0.04 1.00 0.13 0.09 0.08
## ke 0.12 0.28 0.13 1.00 0.39 0.34
## pg 0.04 0.33 0.09 0.39 1.00 0.49
## yv 0.34 0.69 0.08 0.34 0.49 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 644.2863
##
## Estimates
## loc scale shape
## 8.948 8.391 0.153
##
## Standard Errors
## loc scale shape
## 1.03278 0.80137 0.08555
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 28
## Gradient Evaluations: 10
##
##
## Tail behavior based on shape parameter (0.153): Heavy-tailed
total precipitation
##
## Spearman correlation matrix
## year fn ab ke pg yv
## year 1.00 0.15 -0.05 0.04 -0.10 0.02
## fn 0.15 1.00 0.11 0.07 0.16 0.13
## ab -0.05 0.11 1.00 0.55 0.25 0.87
## ke 0.04 0.07 0.55 1.00 0.29 0.53
## pg -0.10 0.16 0.25 0.29 1.00 0.35
## yv 0.02 0.13 0.87 0.53 0.35 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 586.8946
##
## Estimates
## loc scale shape
## 17.3640 12.5708 0.1392
##
## Standard Errors
## loc scale shape
## 1.7883 1.4111 0.1245
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 15
## Gradient Evaluations: 8
##
##
## Tail behavior based on shape parameter (0.139): Heavy-tailed
avgexc
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.18 0.19 0.34 0.02 0.16
## ab 0.18 1.00 -0.04 0.20 0.43 0.59
## fn 0.19 -0.04 1.00 0.07 0.16 0.07
## ke 0.34 0.20 0.07 1.00 0.24 0.26
## pg 0.02 0.43 0.16 0.24 1.00 0.33
## yv 0.16 0.59 0.07 0.26 0.33 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 292.314
##
## Estimates
## loc scale shape
## 2.3826 1.3209 -0.2067
##
## Standard Errors
## loc scale shape
## 0.15470 0.10314 0.04652
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 44
## Gradient Evaluations: 11
##
##
## Tail behavior based on shape parameter (-0.207): Short-tailed
Abbotsford
maxEHF
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.46 0.12 0.12 0.04 0.34
## ab 0.46 1.00 0.04 0.28 0.33 0.69
## fn 0.12 0.04 1.00 0.13 0.09 0.08
## ke 0.12 0.28 0.13 1.00 0.39 0.34
## pg 0.04 0.33 0.09 0.39 1.00 0.49
## yv 0.34 0.69 0.08 0.34 0.49 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 689.0903
##
## Estimates
## loc scale shape
## 12.9259 10.1461 0.2749
##
## Standard Errors
## loc scale shape
## 1.24486 1.03254 0.09072
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 28
## Gradient Evaluations: 12
##
##
## Tail behavior based on shape parameter (0.275): Heavy-tailed
total precipitation
##
## Spearman correlation matrix
## year fn ab ke pg yv
## year 1.00 0.15 -0.05 0.04 -0.10 0.02
## fn 0.15 1.00 0.11 0.07 0.16 0.13
## ab -0.05 0.11 1.00 0.55 0.25 0.87
## ke 0.04 0.07 0.55 1.00 0.29 0.53
## pg -0.10 0.16 0.25 0.29 1.00 0.35
## yv 0.02 0.13 0.87 0.53 0.35 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 804.3157
##
## Estimates
## loc scale shape
## 122.5257 69.0880 -0.1185
##
## Standard Errors
## loc scale shape
## 9.2367 6.5460 0.0822
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 35
## Gradient Evaluations: 22
##
##
## Tail behavior based on shape parameter (-0.119): Short-tailed
avgexc
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.18 0.19 0.34 0.02 0.16
## ab 0.18 1.00 -0.04 0.20 0.43 0.59
## fn 0.19 -0.04 1.00 0.07 0.16 0.07
## ke 0.34 0.20 0.07 1.00 0.24 0.26
## pg 0.02 0.43 0.16 0.24 1.00 0.33
## yv 0.16 0.59 0.07 0.26 0.33 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 305.6872
##
## Estimates
## loc scale shape
## 3.6098 1.4094 -0.1845
##
## Standard Errors
## loc scale shape
## 0.16484 0.10960 0.04615
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 37
## Gradient Evaluations: 13
##
##
## Tail behavior based on shape parameter (-0.184): Short-tailed
Prince George
maxEHF
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.46 0.12 0.12 0.04 0.34
## ab 0.46 1.00 0.04 0.28 0.33 0.69
## fn 0.12 0.04 1.00 0.13 0.09 0.08
## ke 0.12 0.28 0.13 1.00 0.39 0.34
## pg 0.04 0.33 0.09 0.39 1.00 0.49
## yv 0.34 0.69 0.08 0.34 0.49 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 703.4146
##
## Estimates
## loc scale shape
## 13.553 12.148 0.107
##
## Standard Errors
## loc scale shape
## 1.535 1.185 0.100
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 21
## Gradient Evaluations: 7
##
##
## Tail behavior based on shape parameter (0.107): Heavy-tailed
total precipitation
##
## Spearman correlation matrix
## year fn ab ke pg yv
## year 1.00 0.15 -0.05 0.04 -0.10 0.02
## fn 0.15 1.00 0.11 0.07 0.16 0.13
## ab -0.05 0.11 1.00 0.55 0.25 0.87
## ke 0.04 0.07 0.55 1.00 0.29 0.53
## pg -0.10 0.16 0.25 0.29 1.00 0.35
## yv 0.02 0.13 0.87 0.53 0.35 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 636.2443
##
## Estimates
## loc scale shape
## 52.44202 20.31190 -0.08282
##
## Standard Errors
## loc scale shape
## 2.73440 1.94527 0.08887
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 25
## Gradient Evaluations: 15
##
##
## Tail behavior based on shape parameter (-0.083): Short-tailed
avgexc
##
## Spearman correlation matrix
## year ab fn ke pg yv
## year 1.00 0.18 0.19 0.34 0.02 0.16
## ab 0.18 1.00 -0.04 0.20 0.43 0.59
## fn 0.19 -0.04 1.00 0.07 0.16 0.07
## ke 0.34 0.20 0.07 1.00 0.24 0.26
## pg 0.02 0.43 0.16 0.24 1.00 0.33
## yv 0.16 0.59 0.07 0.26 0.33 1.00
##
## Call: fgev(x = data[[station]])
## Deviance: 306.4789
##
## Estimates
## loc scale shape
## 3.0860 1.4730 -0.2591
##
## Standard Errors
## loc scale shape
## 0.17273 0.11570 0.05068
##
## Optimization Information
## Convergence: successful
## Function Evaluations: 46
## Gradient Evaluations: 12
##
##
## Tail behavior based on shape parameter (-0.259): Short-tailed
